Research: exact two-port clean-cache cost obstruction

[1337isnot1337]

Result

A clean scratch cache that carries one read-only source contribution across exactly two output ports cannot improve the local transport bill when both the load and exact restore are charged. For source, scratch, and output frames F,H,G_j, let a=dim(F+H), b_j=dim(H+G_j), and d_j=dim(F+G_j). The dimension identity gives a+b_j >= d_j. For every 0<s<1, monotonicity and subadditivity give d_j^s <= a^s+b_j^s. Summing over two ports proves

cache  = 2*a^s + b_1^s + b_2^s
       >= d_1^s + d_2^s = direct.

The result screens one-source/two-output routing only. The direct term is an optimistic local comparator, not a claim that those two channel transfers form a legal full supplier. This does not rule out multi-source coding, changed support or frames, or another nine-array program, and it makes no supplier-admission or new-kappa claim.

A Q^15 coordinate-span control has a=6, b_j=8, d_j=13. At s=9983/10000 the exact intervals show the two-output cache costs 27.907043 versus 25.886876 direct, while for three outputs the cache costs 35.878812 versus 38.830314 direct. This confirms the port-count restriction matters. A separate negative control shows that omitting restoration would falsely predict a two-port saving.

Verification

• python3 -I -B research/complex-clean-cache-seed9df789/verify.py passes all 220,480 positive rank triples through 64 at both s=9983/10000 and 999/1000, plus the exact coordinate-span and omitted-restore controls.
• python3 scripts/research_package.py --package research/complex-clean-cache-seed9df789 --check-only passes source and package metadata pins.
• make selected-record-check passes; selected kappa remains 836330098538459/500000000000000000.
• Local Python 3.12 is unavailable; Python 3.14.7 ran the exact verifier. The registered Python 3.12 package workflow remains the replay target.

Scope and overlap

Track complex-mechanisms, task complex-new-helper-inventory, seed 9df78911476a397cf5f04ebb271934af, priority revision 3, scope key 5868e5281a1e63d41a22; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

The refreshed overlap scan at 2026-10-14 08:51 UTC paginated 431 open PRs and found no exact-scope match. Discussion refresh remained rate-limited; the cached 383-record snapshot is from 08:34 UTC and is not current. Relevant open neighbors were rechecked immediately before submission: #1517 head c8e37d5d0276f8ddd01d9a242cdccba0f44ddbbd, #1348 head 74768ab408b1ae2ce2c7094b49457a86fcb06e94, #1605 head 488f2ecf1835c6d813e96543656dddf0062fdc9a, and #1633 head 652264fa1f70820139b2730363a0056b7fadc689; they study fixed-inventory cross-block mixing, coverage-law thresholds, rank-one reblocking, and E8 decoder ranks, respectively. No advance claim was posted because Discussion API access was unavailable; the local claim records this limitation.

The proof and package pin the selected record, its actual review, source manifest, assembly certificate and reproduction target, plus the fixed-block theorem and exact interval routines. Prepared by Cinna Davis with substantial OpenAI Codex assistance in the derivation, verifier, source pinning, and writing. No independent human review is claimed.

[Mister-Meeseeks]

Batch review at b78859dd6f0d07bf1dda81718a18102bfec9cccb.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Subspace triangle inequality and concave-power subadditivity rule out an individually restored clean scratch cache improving the two-output channel comparator. Exact interval controls and a three-output counterexample delimit scope; multichannel coding and actual full-supplier legality are not covered.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.